Shifts in the apparent depth of a repetitive pattern or texture occur when the eyes are stably converged at a position in front of the pattern. Observations on this phenomenon, known as the Wallpaper illusion, have been made for almost three centuries. Here, we examined whether stereoacuity follows the shifts in the apparent depth of the pattern. The repetitive pattern for our study was a vertical 3cpd-grating segment, 6 deg wide and 2deg high. As we have previously reported, this segment is initially matched at the disparity of the ‘edges’, meaning the starting and ending positions of the segment. However, if the observer converges for several seconds on a fixation point presented in front of and 30′ below the segment, the segment shifts forward in depth by an even multiple of the period. For example, if the edges specify an uncrossed disparity corresponding to 15′ (3/4 period), the segment shifts forward to a crossed disparity of 5′ (1/4 period). Observers signaled when this shift occurred; at that point, we extinguished the fixation point, and 500 msec later presented a test probe at various disparities. The observer judged the relative disparity of the test with respect to the grating. Stereoacuity was always best in the plane corresponding to the perceived depth of the segment, whether at the ‘edges’ or at the new forward match. Thus, without any change in the stimulus, stereo sensitivity underwent dramatic changes triggered by perceptual shifts to alternative matches.